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Why do charged particles sometimes follow helical paths in magnetic fields?
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Magnetic fields and the levels of magnetism of particles, atoms, crystals, and domains.
Charged particles follow helical paths in a magnetic field due to the nature of the Lorentz force, which acts on a particle moving with velocity v through a magnetic field B.12
The magnetic force is proportional to the vector cross product of the particle's velocity and the magnetic field. This force is always directed perpendicular to both the velocity and the magnetic field. When the angle between the velocity and the magnetic field is less than 90°, the particle's motion can be decomposed into two components:12
- Parallel component: The particle continues to move undeflected along the magnetic field lines because there is no magnetic force acting in that direction.12
- Perpendicular component: The magnetic force acts as a centripetal force, causing the particle to follow a circular trajectory in the plane perpendicular to the field lines.12
The combination of constant linear motion along the field lines and circular motion around them results in a helical path, with the axis of the helix running parallel to the magnetic field lines.12